This project is based on the immersed boundary method, an algorithm that was originally designed for the study of flow patterns around heart valves but which has evolved into a generally useful method for problems arising in biological and in technological fluid dynamics. The project involves numerous improvements and extensions of the immersed boundary method, its continued application to cardiac fluid dynamics, and the production of immersed boundary software to serve the larger community of potential users of the immersed boundary method. The immediate aims of the project are to improve the physiological and anatomical realism of a 3D model of the heart, to use the 3D heart model in studies of cardiac disease, to initiate studies of the motion of cerebro-spinal fluid in the brain, to initiate a methodological change involving non-uniform computational lattices, and to implement a distributed-memory parallel version of the immersed boundary method.